WordPress Accessible Keyboard Menus

With that structure, try this:

(note this makes assumptions about your base styles)

// your working styles, trimmed down
#menu-main-navigation li > ul.sub-menu { display: none; }
#menu-main-navigation li:hover > ul.sub-menu { display: block; }

// focus is on the link, not the li!
#menu-main-navigation li a:focus + ul.sub-menu { display: block; }

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